Final answer:
Solutions to a quadratic equation relate to a graph by representing the x-coordinates of the points where the graph intersects the x-axis, the shape of the graph being a parabola, and the y-intercept of the graph.
Step-by-step explanation:
Solutions to a quadratic equation relate to a graph in several ways:
- The solutions are the x-coordinates of the points where the graph intersects the x-axis. If a quadratic equation has two real solutions, the graph will intersect the x-axis at two points. If the quadratic equation has one real solution, the graph will intersect the x-axis at one point (the vertex of the parabola). And if the quadratic equation has no real solutions, the graph will not intersect the x-axis at all.
- The shape of the graph itself is a parabola. The vertex of the parabola is located at the point (h, k), where h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex. The direction the parabola opens depends on the sign of the coefficient of x^2 in the quadratic equation.
- The y-intercept of the graph is the point at which the graph intersects the y-axis. This can be found by substituting x=0 into the quadratic equation and solving for y.